Contributed by Francis (Skip) Fennel and Jon Wray
Issues related to assessment continue to be a challenge experienced (and often vocally expressed) by many—teachers, administrators, parents/family members, and others. Educators seek to understand and emphasize the role that assessment can and should play in order to impact classroom instruction. When we ask educators, particularly classroom teachers and mathematics specialists/leaders, about assessment, we receive many different responses. Some often refer to assessment as a unique moment—perhaps at the end of the week, unit, or year or a state-mandated assessment—as opposed to an activity directly and continually linked to their planning and teaching.
Formative assessment is of critical importance and should be regularly connected to planning and instruction to improve student learning. Working with our co-author, Beth Kobett, we have developed five formative assessment techniques to guide teaching and learning every day. We call them The Formative Five, and we’ll discuss them briefly below.
Observations—more specifically, the very direct observation of student and class progress during specific mathematics activities—is usually your first stop in formative assessment. Ultimately, your intent is to link what you observe to your planning and teaching directly; the former should influence the latter. While the most readily used, it has been our experience that observation is also the most taken for granted and, to an extent, the least understood of our five techniques. This formative assessment technique requires that you quickly analyze what you observe into actionable tasks within your planning and teaching. Some key considerations and guiding questions, related to the use of observations, include the following:
- What would you expect to observe?
- How would you know “it” if you saw it?
- What misconceptions might you observe?
- How might you record and provide feedback of what you observed?
Interviews have long been used in mathematics education. When used as a formative assessment technique (note that the intent is not as a clinical interview, nor is the interview deficit based), this “check-in” is an opportunity to dig deeper in a one-to-one or small-group setting. Interviews provide useful insight into what a child is thinking and often extend use of the observation technique. Consider the following general framework to guide your interviews for a problem, task, or exercise:
- How did you solve that?
- Why did you solve it that way?
- What else can you tell me about what you did?
3. Show Me
We created the Show Me technique because of the assessment potential of on-the-spot teacher prompts. Show Me combines elements of the observation and the interview. Often, this technique extends and deepens observations and includes questions that teachers might have asked in an interview. The Show Me is performance based, and teachers often use it to assess the extent to which students can represent important mathematics concepts. The Show Me technique also supports and encourages differentiation.
4. Hinge Questions
The hinge question is used to gauge the impact of a lesson. Next steps,planning and instruction-wise “hinge” on responses to this question. The hinge question typically occurs near the end of the lesson or at a “hinge point” within the lesson. As noted, the hinge question is that “deal-breaker question” for any lesson, since success of any given lesson hinges on the responses to the question. Responses indicate whether a teacher can move from one important idea or concept to the next. As such, a hinge question impacts both planning and instruction. Here are a few guidelines to consider when developing hinge questions:
- Design hinge questions that elicit the right response for the right reason.
- When using multiple-choice hinge questions, incorrect responses should be interpretable.
- It should take about 2 minutes to ask the hinge question and consider student responses.
5. Exit Tasks
The exit task, our final formative assessment technique, is a capstone problem or task intended to capture a significant focus of the day’s lesson (or perhaps several days). Very intentionally, the exit task is not described as an exit ticket; rather, the task is a problem or activity that engages students and captures the intent of the lesson. Such tasks are not trivial. Combined with the hinge question, the exit task should provide mathematical closure to your lesson and help shape your planning for the next day.
We hope you find these techniques useful and find ways to implement them in your classroom—daily! Formative assessment is integral to planning and teaching—what you do every day! The Formative 5 serve to provide defined, classroom-validated assessment techniques that truly inform planning and instruction. Below are more resources we think you may find helpful.
Skip Fennell and Jon Wray are authors of enVisionmath2.0 Grades K–8. View their full recorded webinar here:
Fennell, Francis (Skip), Beth McCord Kobett, and Jon A. Wray. 2017. The Formative 5: Everyday Assessment Techniques for Every Math Classroom. Foreword by Matt Larson. Thousand Oaks, CA: Corwin Mathematics/National Council of Teachers of Mathematics.
The link below provides access to information related to the recently released eCourse related to the Formative 5.